GM Miscellaneous
Random GM Miscellaneous Notes Various bits of information and math in the background of the game. Sight Distances Human eyes have an angular resolution of 0.0003 radians, so that's the minimum size of a "pixel". The distance to resolve an item of length s is s/tan(0.0003) basic trig, right?, and tan(0.0003) is 0.0003 to 7 significant digits. So with reasonable light, you can tell that someone has a head on top of their body (~6" wide) from 2000' away, though it's in distinct blur at that range. More pixels are needed to make better distinction (see here for more details). More pixels smaller length s, so divide s by the pixel count. Magnification decreases effective distance by the magnification factor, so if you're standing 400' away from someone and looking at them with 8x telescope, it's as though you were looking at them from 25' away. So while the guy without a 'scope standing next to you can definitely say that he's looking at someone with a face, you and your telescope can say that it's "Bob the Miller." I put together some images that illustrate this nicely; I should upload them soon. Spotting Ranges ;Spotting ranges for the human eye Some things need to be recognized or ID by using much smaller objects: each man in an infantry regiment might be visually distinct at 4000', but the colors on their surcoats are only 2-3' long and can't be fully identified at more than 500'. Dust, wind, rain, and intervening terrain shorten sightlines. The horizon is sqrt(1.5*height in ft) miles away, so roughly 3 miles for a standing man, 4 miles for a cavalryman, 9 miles for a flyer at 50', 20 miles for a flyer at 300', and 30+ for flyers at higher elevations. Normal air and dust cuts maximum distance to about 20 miles, regardless of visual acuity, but on clear days people can see up to 80-100 miles away if the object is above the horizon and more than 500' across. GURPS Mechanics Proposed, anyway. You can distinguish items from the background a distance of of (objects SM + 20) on the linear measurement of the SSR table yds away, so an SM+0 target can be seen, maybe, at 5,000 yards. At more than SM +15 yards, roll Vision, Observation, or Perception, with a penalty equal to twice the difference between the SSR range value and 15 - ie, -2 at 1000 yds, -6 at 2000 yds. You can recognize an item as a general type of thing at SM +13 yards, so 300 yds to say that the blur on the horizon is "a man, or an elf" as opposed to "a bear." Success on a Vision, Observation, or Perception increases that range to SM +14. You can identify an item as a specific type of thing at SM +11 yards, with a successful test increasing the range by 1. Identifying a person generally means identifying the face (SM -5), so humans can usually do it at 30-50 yards. Magnification divides the effect range by the magnification factor. Category:GM Miscellaneous